Explain the method of Crank-Nicholson from the definition of explicit and implicit methods..
Q.17 Use implicit trinomial tree to perform the calculation of a put knowing the following information: S = 95; X = 106; RF = 0, 05; Sigma = 0.25; T = 5/12; b = 0.12; n = 200.
Q.19 Using the Monte Carlo Least Squares approach, evaluate the price of an Amerian put assuming an Heston (1993, 2000) stochastic volaitiliy model having the following caracteristics: K=10, r=0.05, T=4/12, k=5, theta=0.16, sigma=0.9, rho=0.1, v0=0.0625, S = 8 to 12, and values of American puts : 2.000, 1.107064, 0.520030, 0.213668. Define and explain each concepts. Hint : see Rouah (2015). Q.20 Finite difference methods a) Show how we can tie the methods of finite difference to the trinomial trees. b) Define and explain how we can calculate the first and second derivatives (calculus) by numerical methods. c) Explain the method of Crank-Nicholson from the definition of explicit and implicit methods.
Q.21 Using a variance reduction technique like the antithetic variance reduction method, redo Q.15 and compare your result. Discuss other variance reduction techniques.
Explain the method of Crank-Nicholson from the definition of explicit and implicit methods.